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  • In the binomial expansion of (a-b)n, n > 5, the sum of the 6th and 7th terms is zero, then a/b equals:O

In the binomial expansion of (a-b)n, n > 5, the sum of the 6th and 7th terms is zero, then a/b equals:

Option: 1

\frac{n-5}{6}


Option: 2

\frac{n-4}{5}


Option: 3

\frac{5}{n-4}


Option: 4

\frac{6}{n-5}


Answers (1)

best_answer

T6 = T5+1 = nC5an-5(-b)5 = -nC5an-5 . b5

T7 = T6+1 = nC6an-6(-b)6 = nC6an-6 . b6

\therefore  T5 + T6 = 0

\implies  -nC5an-5 . b5 + nC6an-6 . b6 = 0

\implies \frac{a^{n-5} b^5}{a^{n-6}b^6} = \frac{^{n}C_{6}}{^{n}C_{5}}

            \frac{a}{b} =\frac{n!}{(n-6)! 6!} \frac{5! (n-5)!} {n!} = \frac{n - 5}{6}

Posted by

Riya

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